Reinstall Java 1.6, download the safer 'Offline' Java Installer For Windows: Java Downloads for All Operating Systems
. This is highly important for Windows 7:
Right-click the Java installer and choose Run as Administrator
. You can also do the same with the LW shortcut on desktop after installing Java. Keep that Java installer for now.
See if LW connects. Give it some time.
If LW does not connect, close, and run the Connection Fix program
Just for your information, LW will not run with the Java 1.7 version presently available. Maybe a later release will work with it, once they sort out the java 1.7 bugs.
How long ago did LW connect properly for you?
I forgot to ask, which version of LW are you using?